The unemployed receive the most overpayments
The level of fraud and mistakes made in the benefit system has remained largely unchanged, according to the Department of Work & Pensions (DWP).
It estimates that in 2008-09 about 2% of all national and local government benefits, about £2.7bn, were overpaid due to fraud and mistakes.
At the same time, 0.9% of all the benefits, about £1.2bn, were underpaid.
The DWP said the overpayments and underpayments were similar to those estimated in the previous two years.
The research did not cover tax credits, which are administered by HM Revenue & Customs.
The biggest overpayments - due to fraud, or mistakes by claimants and officials - are thought to have been in income support, job seeker's allowance, pension credit and housing benefit.
The percentage of these benefits overpaid ranged from 4.5% to 5.1%, with the most cash being lost in housing benefit, at £770m.
Carer's allowance is also thought to have suffered a high level of fraud or mistaken payment, at 5.5% of all payments made, although the relatively small sums paid out for this allowance meant the loss was put at just £70m.
The largest state benefit by far is the state pension, with total payments amounting to £61.6bn in 2008-09.
However this suffered the lowest level of apparent fraud and mistaken payments, at just 0.2%% or £100m.
Underpayments in 2008-09 were put at £100m more than in the previous year because of the increase in total benefit payments during that time.
The failure to pay people the correct amount was overwhelmingly due to mistakes by officials and claimants rather than fraud.
The biggest failure to ensure that people received the right money, both in percentage and absolute terms, was detected in disability living allowance.
The DWP said 2.5% of this was underpaid in the past financial year, amounting to £260m.
The department warned that its figures for underpayments did not include those who had failed to make a claim when they entitled to do so.
The DWP carries out its research by statistical analysis of survey data and interviews with selected claimants.
It warned that the results might be affected by sampling errors, and did not purport to detect all fraud or mistakes.
Frauds were by definition largely hidden, and mistakes by officials might be too complex to unravel, the department said.
The DWP pointed out that some overpayments were subsequently paid back, particularly for housing benefit.